The International journal of analytical and experimental modal analysis ISSN NO:0886-9367 A discussion on analytical study of Semi-closed set in topological space 1 Dr. Priti Kumari, 2 Sukesh Kumar Das, 3 Dr. Ranjana & 4 Rupesh Kumar 1 & 2 Guest Assistant Professor, Department of Mathematics Saharsa College of Engineering , Saharsa ( 852201 ), Bihar, INDIA 3 University Professor, University department of Mathematics Tilka Manjhi Bhagalpur University, Bhagalpur ( 812007 ), Bihar , INDIA 4 M. Sc., Department of Physics A. N. College Patna, Univ. of Patna ( 800013 ), Bihar, INDIA
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[email protected] Abstract : In this paper, we introduce a new class of sets in the topological space, namely Semi- closed sets in the topological space. We find characterizations of these sets. Further, we study some fundamental properties of Semi-closed sets in the topological space. Keywords : Open set, Closed set, Interior of a set & Closure of a set. I. Introduction The term Semi-closed set which is a weak form of closed set in a topological space and it is introduced and defined by the mathematician N. Biswas [10] in the year 1969. The term Semi- closure of a set in a topological space defined and introduced by two mathematician Crossley S. G. & Hildebrand S. K. [3,4] in the year 1971. The mathematician N. Levine [1] also defined and studied the term generalized closed sets in the topological space in Jan 1970. The term Semi- Interior point & Semi-Limit point of a subset of a topological space was defined and studied by the mathematician P.